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Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/310361
Description: Let (X, d, μ) be a metric measure space endowed with a distance d and a nonnegative Borel doubling measure μ. Let L be a second order self-adjoint positive operator on L²(X). Assume that the semigroup ... More
Reviewed: Reviewed
Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/278997
Description: We obtain analogues of several recent bounds on the number of solutions of polynomial congruences modulo a prime with variables in short intervals in the case of polynomial equations in high degree ex ... More
Reviewed: Reviewed
Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/220238
Description: One defines a non-homogeneous space (X,μ) as a metric space equipped with a non-doubling measure μ so that the volume of the ball with center x, radius r has an upper bound of the form r n for some n> ... More
Reviewed: Reviewed
Date: 2013
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/272190
Description: We obtain upper bounds on the number of solutions to congruences of the type (x1 + s)... (xv + s) ≡ (y1 + s)... (xv + s) ≢ 0 (mod p) modulo a prime p with variables from some short intervals. We give ... More
Reviewed: Reviewed
Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/271249
Description: We show that for any integers a and m with m ≥ 1 and gcd(a,m) = 1, there is a solution to the congruence pr ≡ a (modm) where p is prime, r is a product of at most k = 17 prime factors and p, r ≤ m. Th ... More
Reviewed: Reviewed
Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/276556
Description: We describe weighted restriction (Plancherel) type estimates and sharp Hebisch-Müller-Stein type spectral multiplier result for a new class of Grushin type operators. We also discuss the optimal expon ... More
Reviewed: Reviewed
Date: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/205033
Description: For a polynomial f∈Fp[X] , we obtain upper bounds on the number of points (x, f (x)) modulo a prime p which belong to an arbitrary square with the side length H. Our results in particular are based on ... More
Reviewed: Reviewed
Date: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/198238
Description: We use a result of É. Fouvry about the distribution of solutions to systems of congruences with multivariate polynomials in small cubic boxes and some ideas of W. Schmidt to derive an asymptotic formu ... More
Reviewed: Reviewed
Date: 2011
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/161737
Description: Monoidal objects (or pseudomonoids) in monoidal bicategories share many of the properties of the paradigmatic example: monoidal categories. The existence of (say, left) duals in a monoidal category le ... More
Reviewed: Reviewed
Date: 2011
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/160272
Description: Categorical universal algebra can be developed either using Lawvere theories (single-sorted finite product theories) or using monads, and the category of Lawvere theories is equivalent to the category ... More
Reviewed: Reviewed
Date: 2010
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/129178
Description: 14 page(s)
Reviewed: Reviewed
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Authors: Lack, Stephen
Date: 2010
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/224987
Description: Categorical orthodoxy has it that collections of ordinary mathematical structures such as groups, rings, or spaces, form categories (such as the category of groups); collections of 1-dimensional categ ... More
Reviewed: Reviewed
Date: 2010
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/128917
Description: We study the distribution of singular and unimodular matrices in sumsets in matrix rings over finite fields. We apply these results to estimate the largest prime divisor of the determinants in sumsets ... More
Reviewed: Reviewed
Date: 2010
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/128910
Description: 10 page(s)
Reviewed: Reviewed
Date: 2009
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/322889
Description: In this paper, we compare some deterministic and probabilistic techniques in the study of upper bounds in problems related to certain mean square discrepancie with respect to balls in the d-dimensiona ... More
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